The half-life of a nuclide is 737 hrs
Let the initial mass of nuclide is N° = 100
The final mass of nuclide after 407 hours
= 100 - 38 = 62
The expression for decay constant is
λ = 1/t ln(N°/Nt)
Substitute the given values and calculate the decay constant as,
λ = 1/407hr ln(100/62)
λ = 9.4 x 10^-4/hr
Now, the half-life is calculated as,
t1/2 = 0.693/λ
= 0.693/9.4 x 10^-4/hr
t1/2 = 737 hrs
Hence, the half-life of a nuclide is 737 hrs
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